Improving Methods to Forecast Mixing Heights at the NWS Raleigh

2012 North Carolina Wildland Fire Alliance and Cooperators Meeting

Jonathan Blaes

Phillip Badgett

Gail Hartfield

01 February 2012

Why Do We Need to Revisit Mixing Heights?

The current methodology used by many forecasters to determine the mixing height is inconsistent and often lacks good science

Verification of operational mixing height forecasts is rare but local verification at RAH suggests a deficiency in the approach and a persistent, large positive bias (error)

RAH will transitioned to hourly mixing heights and transport winds a the end of fall 2011

Good mixing height forecasts will be beneficial to the fire weather community (better pre-suppression forecasts and improved resolution in spot forecasts) and to support an anticipated increase in decision support activities.

Where is this project now?

Solicit the forecast staff for their methodology for determining the mixing height – completed, approaches varied and forecast results were inconsistent

Perform verification analysis of Greensboro mixing height forecasts – completed, persistent over forecast of mixing heights was noted

Determine a preferred methodology for determining the mixing height given an observed sounding – Completed, science indicates that we should not use the current parcel or Holzworth method but rather use vertical profiles of potential or virtual potential temperature with height when available

Improve GFE methods and tools – initial efforts have been completed, tools and procedures have been updated

How have Forecasters Determined the Mixing Height in the Past and How Did It Verify?

May 15, 2010 Subjective Mixing Height Forecast

4,000

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8,000

9,000

10,000

11,000

12,000

Many forecasters at RAH were trained to use the parcel or Holzworth method to identify maximum mixing heights. This technique follows the dry adiabat from the surface forecast maximum temperature up to where the respective adiabat crosses the forecast/observed thermal profile.

In an experiment, RAH forecasters were given the 12 UTC RAOB to the right and an expected high of 91 degrees along with some other synoptic information.

A total of 13 RAH forecasters provided their forecast of maximum mixing height. Takeaway - a wide range of inconsistent solutions was provided.

What is the Mixed-Layer Depth (mixing height)?

Several Definitions in the literature -

“Height of the layer adjacent to the ground over which pollutants or any constituents emitted within this layer or entrained into it become vertically dispersed by convection or mechanical turbulence within a time scale of about an hour” (Siebert et al., 1998)

The mixed-layer depth or mixing height is the depth of the surface based mixed layer which is well mixed due either to mechanical turbulence or convective turbulence.

The atmospheric mixed layer is a zone having nearly constant potential temperature and specific humidity with height. The depth of the atmospheric mixed layer is known as the mixing height.

The planetary boundary layer or mixed-layer consists of three major parts

Convective mixed layer Unstable conditions with strong upward heat flux (typically during the day) from the surface and low wind speeds, the planetary boundary layer is associated with convective mixing. The depth of the mixed layer typically ranges from 1-3 km.

Nocturnal stable boundary layer - Radiational cooling of the air just above surface tends to create a low level inversion with relatively ‘stable’ conditions. The depth of the stable boundary layer and ranges from about 10 m to 500 m deep.

Residual layer - The residual layer is the part of the atmosphere where mixing still takes place resulting from the left-over of convective mixed-layer (CML) and has all the properties of the recently decayed CML.

Mixed-layer height

Methods to Determine the Mixed-Layer Depth from Soundings?

There are several methods to determine the maximum mixing height of the convective boundary layer, but they vary considerably, range in complexity, are subject to their own limitations, and are dependent on the availability and resolution of vertical profile data.

from Seibert et al. (1998)

“Parcel” or “Holzworth”

Richardson Number

“Moisture Decrease”

“Inversion Base”

“Stable Layer”

Methods to Determine the Mixed-Layer Depth from Soundings

Holzworth Method (parcel method) – This method (Holzworth, 1967) calculates the maximum mixing layer depth based on the afternoon surface temperature and the temperature sounding. This method lifts the surface parcel up the dry adiabat from the expected maximum temperature to its intersection with the temperature profile. The mixing height is taken as the equilibrium level of an air parcel with this temperature. It is dependent on the surface temperature and often the existence of a pronounced inversion at the top of the convective boundary layer.

Pros – very simple, estimate is based off of a single observed soundingCons –accuracy strongly dependent on the surface temperature, and a high uncertainty in the estimate MH values may result in situations without a pronounced inversion at the CBL top. Different authors pointed out that the MH determined by the “Holzworth method” is not strongly correlated with some detailed observations.

Methods to Determine the Mixed-Layer Depth from Soundings

Potential Temperature Method - This method first noted by Heffter (1980) analyzes the potential temperature or virtual potential temperature profile for the existence of a critical elevated inversion, which is assumed to indicate the top of the mixing height. The mixing height is at the lower range of a layer containing a positive potential temperature lapse rate. This method allows forecasters to use NWP data more rigorously over the course of the convective day.

Pros – More scientifically rigorous, more accessible to operational forecasters than in the past, includes changes in atmosphere during the convective dayCons – Requires hourly or 3 hourly resolution data, interpretation can be subjective

Methods to Determine the Mixed-Layer Depth from Soundings

Potential Temperature Method Example - The mixing height is associated with an increase in the positive slope of theta or theta-v. For the example below, the vertical plot of theta indicates a mixed layer height of between 3,000 and 3, 300 ft AGL while the Holzworth approach would give a mixing height of around 4,500 ft AGL. Other variables such as the mixing ratio and wind can also highlight the depth of the mixed layer.

Super-adiabatic layer

Top of the mixed layer

Given the limited sample points and allowing for entrainment, the top of the mixed layer could be in this layer

GSO 090504/00 Plot of Theta with height

Inconsistencies in Mixing Height Estimations and Forecasts

Mixing height estimations based on standard radiosonde data may result in rather high uncertainties (Martin et al., 1988).

In cases of a weak inversion or a non-perfectly mixed CBL, the analysis of the same potential temperature profile by several experienced meteorologists may easily result in relative differences of 25% or even larger (e.g., Hanna et al., 1985; Martin et al., 1988).

Special problems occur for the stable nocturnal boundary layer since no universal relationship seems exists between the profiles of temperature, humidity, or wind and turbulence parameters.

NWP models typically have a high bias in both the convective boundary layer and especially the nocturnal stable boundary layer depth (Cuxart 2006). This error likely results from parameterization issues and turbulence values that are too large. Foe example, the WRF code has several instances in which statements are included to keep the turbulence > 0.

NWP forecasts typically show a rather smooth potential temperature plot with height. Observed soundings can detect short lived variances in plots of potential temperature plot with height. These irregular plots with “kinks” in them most often occur during the convective mixing.

Take Away Message – the what and how’s of the mixed layer

The mixed-layer depth or mixing height is the depth of the surface based mixed layer which is well mixed due either to mechanical turbulence or convective turbulence. This layer has a nearly constant potential temperature and specific humidity with height.

The planetary boundary layer or mixed-layer consists of three major parts

There are several methods to determine the maximum mixing height of the convective boundary layer, but they vary considerably, range in complexity, are subject to their own limitations, and are dependent on the availability and resolution of vertical profile data.

We used the Potential Temperature method through the remaining portion of this project and advocate it use operationally. This method defines the mixed layer height as is associated with a significant increase in the positive slope of theta or theta-v.

Mixing height estimations based on standard radiosonde data may result in rather high uncertainties. In cases of a weak inversion or a non-perfectly mixed CBL, these uncertainties can reach differences of 25% or larger.

NWP models typically have a high bias in both the convective boundary layer and especially the nocturnal stable boundary layer depth

Verification of Mixing Height Forecasts at Greensboro

Forecasts of the daily maximum mixing height for the Guilford County, NC fire weather zone from 1 May 2009 through 30 April 2010 were subjectively verified using the KGSO RAOB and the potential temperature method.

A poster sharing more complete results is available on the RAH science page at this link – Verifying Forecasts of Maximum Mixing Height for Greensboro

Observed mixing heights over the course of the year showed large day-to-day variability due to seasonal, synoptic, and mesoscale conditions.

The average mixing height during the 327 days of available data was 3,566 feet, which is close to the average of 4,133 feet computed across 4 southeast U.S. sites by Garrett (1981).

Verification of Mixing Height Forecasts at Greensboro

For first period forecasts, the average first period mixing height error during the 327 study days, was 1,487 feet with a mean absolute error of 58%.

A total of 12 days had errors in excess of 4,000 feet, 42 days had errors of more than 3,000 feet, and 102 days (nearly a third) had errors of 2,000 feet or more.

For first period forecasts, 239 days out of 327 (73.1%) verified too high, while 80 days (24.5%) were too low.

Maximum mixing height forecasts consistently verified too high across all four forecast periods.

A very large fraction of forecasts in excess of 6,000 feet were too high.

Verification of Mixing Height Forecasts at Greensboro

The greatest observed mixing height was 9,600 feet on April 12th, with three other days experiencing mixing heights between 8,000 and 8,900 feet.

Only 7 days had mixing heights greater than 7kft and 23 days had mixing heights greater than 6kft.

The average monthly observed mixing heights during this one year period were greatest in April and smallest in December. This is similar to Garrett (1981) which showed a max in March and April and a minimum in December and January.

Climatology and Verification Summary

The average mixing height (MH) for the whole year was 3,566 feet.

The average monthly observed MH greatest in April and smallest in December. Garrett (1981) showed a max in March and April and a minimum in December and January.

Only 4 days had a mixing height > 8,000 feet, only 7 days had MHs greater than 7,000 feet and 23 days had MHs greater than 6,000 feet.

The MH ranged between 2,000-4,999 feet during 196 days (60%) (target range)

The MH ranged between 1,000-5,999 feet during 285 days (87%) (need a good reason to be outside of this range)

The average first period MH error was 1,487 feet (MAE 58%)

12 days had errors in excess of 4,000 feet, 42 days had errors of more than 3,00 feet, and 102 days (nearly a third) had errors of 2,000 feet or more.

First period forecasts were too high nearly three quarters of the time (73.1%) of the time.

Take Away Message - verificationThe average mixing height (MH) for the whole year was 3,566 feet.

The average monthly observed MH greatest in April and smallest in December. Garrett (1981) showed a max in March and April and a minimum in December and January.

Only 4 days had a mixing height > 8,000 feet, only 7 days had MHs greater than 7,000 feet and 23 days had MHs greater than 6,000 feet.

The MH ranged between 2,000-4,999 feet during 196 days (60%) (target range).

The MH ranged between 1,000-5,999 feet during 285 days (87%) (need a good reason to be outside of this range)

The average first period MH error was 1,487 feet (MAE 58%). A total of 12 days had errors in excess of 4,000 feet, 42 days had errors of more than 3,00 feet, and 102 days (nearly a third) had errors of 2,000 feet or more.

First period forecasts were too high nearly three quarters of the time (73.1%) of the time.

Example vertical distributions of theta, wind, and mixing ratio for typical daytime (convective) and nighttime (stable) scenarios

Super-adiabatic

Nearly adiabatic

Strongly stable lapse rate

Strongly stable lapse rate

Nearly adiabatic

Weakly stable lapse rate

Theta Wind Mixing ratio

Top of the mixed layer

Nocturnal stable layer Adapted from Stull, R. B., 2000: Meteorology for Scientists and Engineers

Example of the observed convective mixed-layer over land

Vertical sounding of virtual potential temperature and mixing ratio. Subjectively analyzed mixed layer height (black dashes).

Vertical sounding showing reflectivity height (colors) and analyzed mixing height (white line). Black crosshairs correspond to times in figure above.

Example from 4 Aug, 1996 in Champaign–Urbana, IL.

from Angevine (2008)

Idealized evolution of potential temperature during the day and night for convective and stable nocturnal scenarios

Note the dramatic jump in mixing heights in the summer during the morning between 900 am and noon.

The increase in mixing height slows afternoon.

The morning increase in mixing height is more gradual and linear during the winter daytime.

The nocturnal stable layer is longer during the winter than summer.

Summer

Winter

Idealized evolution of potential temperature during the day and night for convective and stable nocturnal scenarios

Note the greater mixed layer depth in the summer and the longer period of mixing compared to the winter. FA – free atmosphere ML – mixed layer RL – residual layer SBL – stable boundary layer CI – capping inversion EX – entrainment zone

Summer

Winter

Identifying an appropriate mixing height at night with the stable nocturnal boundary layer is difficult.

While the actual depth of the stable nocturnal boundary layer increases overnight, the resultant mixing height remains very shallow. In other words, while the depth of the surface based inversion may grow, the stable layer still originates at the surface, resulting in a shallow mixing depth.

In the example to the lower right, an analysis of LLJ heights across Kansas, which should correspond to the top of the stable boundary layer is shown. The mode and the median are in the 80-100 m range.

A De facto value of 250 feet has been accepted for the height of the nocturnal stable layer.

Stable nocturnal layer

Adapted from Banta et al., 2002

Hei

ght (

ft)

Time (hours)9AM 12PM 3PM 6PM 9PM 12AM 3AM

1kft

6AM

sunsetsolar noonsunrise

3AM

2kft

5kft

4kft

3kft

Mixing heights increase 1-2 hours after sunrise.

Maximum mixing height occurs between 1-2 hours after solar noon.

New stable boundary layer develops 1-2 hours before sunset.

Mixing height decreases very slightly after peaking

Maximum mixing height increase is dependent on time of year, atmospheric profile, as well as synoptic and mesoscale conditions.

Idealized Diurnal Mixing Height Curve

The idealized mixed layer height cartoon below highlights the relationship of the mixing height with the solar cycle.

Take Away Message – observed and idealized diurnal patterns

The mixed layer depth can often be identified in three variables (theta, wind, and mixing ratio or specific humidity). The profiles and distribution of these three variables will vary between the convective and nocturnal stable layer.

The idealized potential temperature examples, show a dramatic jump in mixing heights in the summer during the morning between 900 am and noon with the increase slowing during the afternoon. During the winter, the morning increase in mixing height is more gradual and linear.

The nocturnal stable layer is more apparent and longer during the winter longer winter nights than summer.

Mixing heights increase 1-2 hours after sunrise. Maximum mixing height occurs between 1-2 hours after solar noon. New stable boundary layer develops 1-2 hours before sunset.

The diurnal mixing height curve is not usually bell shaped. Rather, the mixing height peaks a little after solar noon and then reforms at the surface a little before sunset.

A De facto value of 250 feet has been accepted for the height of the nocturnal stable layer.

AWIPS Procedure

AWIPS procedure “4___b. FireWx” under the wforah account has been updated

Added various plots of potential and virtual potential temperature for observed and forecast data

Unfortunately BUFR soundings will not display potential and virtual potential temperature with a vertical coordinate of feet AGL or even MSL. Terry opened AWIPS DR 21333 to get this bug fixed.

Model derived soundings for points in D2D will provide potential and virtual potential temperature with a vertical coordinate of feet AGL but at a reduced temporal resolution (3 hour for NAM12 and 6 hour for NAM40 and GFS40)

AWIPS does not provide ideal plots of potential temperature at a sufficient temporal resolution

Because of AWIPS limitations, we will need to augment our forecast with other sources and displays of forecast profiles.

Hourly BUFR soundings in AWIPS can display Skew-T data.

The Bufkit Skew-T display can be very helpful.

Do not focus on the temperature alone, but rather the T, Td, and wind distribution. Oftentimes, the Td will be best indicator of the top of the convective mixed layer, note when the Td trace stops following the mixing ratio lines.

Recommended Strategy to Determine Mixed Layer Depth*

1) Let climatology set the starting point- Use seasonal and monthly climatological values along with the extremes to set a likely range of mixing heights

2) Pattern recognition via observed and plan views of model forecast data looking for…- cloudy/deeply moist/rainy days will usually have much lower mixing depths relative to sunny ones.- northeasterly low level flow: typically shallower mixing, often with a subsidence inversions aloft. - deep westerly flow (at least through H85-7) typically yields deeper mixing, which seems to increase with

increasing wind speeds through that layer.

3) Examine observed and forecast soundings - get an idea of previous days mixing heights (useful for stagnant patterns/persistence forecasts) and the

characteristics of the simulated thermal/moisture profile. - examine the characteristics of the forecast thermal/moisture profile. Examine the degree of inversion aloft and

how deeply the model mixes the boundary layer, evident by relatively constant potential or virtual potential temperature and mixing ratio.

4) ConfidenceConfidence in mixing height can be higher on relatively clear days, when low level lapse rates are steeper and low

level thermal profile should be less prone to error induced by clouds, less steep low level lapse rates, and cooler surface temperatures.

5) Use GFE Tools to Sketch in the Mixing HeightThe “Mixing Height” or “MaxMixing Height” tool in GFE often yields the most representative mixing heights. It can

be used to create background grids before some smoothing/manipulation. Try using the tool for both the GFS and NAM for comparative purposes.

* Thanks MWS

Actually Creating Mixing Height Grids in GFE

The long delayed transition to hourly mixing heights and transport winds at RAH will allow forecasters to more accurately note the changes in mixing height with sunrise, sunset, etc.

A recommended and locally developed methodology for fair weather convective mixing has resulted in two new GFE grids

MaxMixHgt – maximum convective mixing height in feet

NoctMinMixHgt – minimum mixing height observed during the nocturnal stable layer in feet

The recommended methodology for fair weather convective mixing uses the Diurnal_MixHgt_from_Max_Min_MixHgt tool located under the Populate menu

The tool provides the time of sunrise, sunset, and solar noon in the upper left

The forecaster selects the number of hours before or after sunrise, solar noon, and sunset in which the structure of the convective mixed layer changes.

The tool will then try to recreate the diurnal mixing height pattern shown to the right.

Unfortunately, the tool currently uses a linear interpolation for the curve between sunrise to the time after solar noon (working on this, bigger deal in summer)

Overview of Creating Mixing Height Grids in GFE

* Tom Mazza at WFO RLX produced this tool for RAH

1. Edit/create the NoctMinMixHgt grids for the 48 hour forecast period. Research and local convention suggests that 250 feet is a reasonable number for nights with little turbulence and typical radiational cooling. The NoctMinMixHgt_Set_250 tool quickly sets the grid to 250 feet. The NoctMinMixHgt_from_Wind tool estimates the NoctMinMixHgt based on turbulence from the wind grids and will typically produce NoctMinMixHgt values between 250 and 750 feet.

2. Edit/create the MaxMixHgt for the 48 hour forecast periodFollow the recommended strategy to determine mixed layer depth noted earlier (pattern recognition, examining the observed and forecast soundings, noting confidence, and using GFE tools). Use the MaxMixing_Height tool to sketch in a base grid and then make modifications using the strategy above.

3. Click and highlight the desired period of MixHgt grids in the grid editor (select time)This will typically cover the 3 or 4 forecast periods needed for that package. For the morning package select time out to and including 00 UTC in period 3 (~36 hours). For the afternoon package select time out to and including 00 UTC in period 4 (~48 hours).

Summary of Steps to Actually Create Mixing Height Grids in GFE

4. Run the Diurnal_MixHgt_from_Max_Min_MixHgt tool from the Populate menu. The tool will prompt the forecaster for the time in which sunrise, solar noon, and sunset impact the diurnal pattern of mixing height. These values default to the climatological norm, adjust them as necessary.- Mixing typically begins 1 hour after sunrise- Maximum mixing height typically is reached 2 hours after solar noon- Nocturnal stable layer typically develops one hour before sunsetReasons to adjust these climatological values include precipitation, cloud cover impacting insolation or radiational cooling, frontal passes, thermal advection, winds producing turbulence, and more.

5. The tool will create hourly mixing height grids during the time period selected in step 3.

6. Be sure to check and adjust the changes in mixing height during the morning hours so as to improve upon the linear interpolation. This will often require some hand editing. Keep in mind that the evolution of the mixed layer in the morning is typically driven by convective mixing which is modulated by seasonality and the amount of insolation among other factors.

Summary of Steps to Actually Create Mixing Height Grids in GFE

Actually Creating Transport Winds in GFE

1. The first step is to create the hourly mixing height gridsTransport winds cannot be created until the mixing height is resolved.

2. Highlight the appropriate time period and run the Create_TransWinds_from_Algorithm toolThis model driven tool will populate the transport wind grids every 3 or 6 hours depending on the model selected. The procedure compares the MixHgt grid first and then computes the TransWind grids. The forecaster will need to interpolate between edited grids.

3. Adjust transport winds for nighttime periods with a stable nocturnal layerWhen a nocturnal stable layer is present, the transport winds will be very close to the surface wind with some adjustment to the wind direction to account for reduced friction and perhaps a slight increase in velocity. Use the Copy_Wind_IntoTransportWind tool to copy the surface wind into the TransWind grid. Finally, use the Veer_the_Wind tool once to decrease the effect of surface friction on the TransWind direction.

Example case from 05 September 2009

Other things to rememberSampling forecast Skew-T plots in AWIPS provides the height in feet above MSL (need to adjust the height for the location to produce AGL [GSO (-926 ft), RDU (-435 ft), FAY (-189 ft), GSB (-109 ft), and KRWI (-159 ft)

3,980 feet on the AWIIPS variable with height vs. 4,848 feet on the AWIPS Skew-T

Other things to rememberThe algorithm used in the Bufkit time-height plots of mixing height use a form of the parcel method with the max temperature, not the best choice

3,400 feet

5,500 feet

Still to come

Feedback from the RAH staff will be used to make improvements to the methodology

A reference documenting the setup and algorithm used in GFE smartinits and tools to produce the mixing height

Improvements to the interpolation scheme used in the Diurnal_MixHgt_from_Max_Min_MixHgt procedure

Acknowledgements

Dr Basu at NC State was helpful with various parts of the micrometeorology and PBL science

Whitney Rushing, performed a tremendous amount of data collection and cataloging.

Tom Mazza at RLX developed the Diurnal_MixHgt_from_Max_Min_MixHgt for RAH

References

Angevine, W.M., 2008: Transitional, entraining, cloudy, and coastal boundary layers. Acta Geophysica, 56, 2-20.

Banta, R. M., R. K. Newsom, J. K. Lundquist, Y. L. Pichugina, R. L. Coulter, and L. J. Mahrt, 2002: Nocturnal low-level jet characteristics over Kansas during CASES-99. Bound.-Layer Meteor., 105, 221–252.

Cuxart, J., and Coauthors, 2006: Single-column model intercomparison for a stably stratified atmospheric boundary layer. Bound.-Layer Meteor., 118, 273–303.

Garrett, A.J., 1981: Comparison of observed mixed layer depth to model estimates usingobserved temperature and winds, and MOS forecasts. J. Appl. Meteorol., 20, 1277-1283. Hanna, S.R., Burkhart, C.L., Paine, R.J., 1985. Mixing height uncertainties. Proceedings of 7th AMS Symposium on Turbulence and Diffusion, Boulder, pp. 82-85.

Holzworth, C.C., 1967: Mixing depths, wind speeds and air pollution potential for selected locations in the United States. J. Appl. Meteorol., 6, 1039-1044. Marsik, F. J., K. W. Fischer, T. D. McDonald, and P. J. Sampson, 1995: Comparison of methods for estimating mixing height used during the 1992 Atlanta Field Intensive. J. Appl. Meteor., 34, 1802–1814.

References

Martin, C. L., D. Fitzjarrald, M. Garstang, A. P. Oliveira, S. Greco, and E. Browell, 1988: Structure and growth of the mixing layer over the Amazonian rain forest. J. Geophys. Res., 93, 1361–1375.

Seibert, P., F. Beyrich, S. E. Gryning, S. Joffre, A. Rasmussen, and P. Tercier, 2000: Review and intercomparison of operational methods for the determination of the mixing height. Atmos. Environ., 34, 1001–1027.

Seibert, P., Beyrich, F., Gryning, S.-E., Joffre, S., Rasmussen, A., and Tercier, Ph.: Mixing height determination for dispersion modelling, Report of Working Group 2, in: Harmonization in the Preprocessing of meteorological data for atmospheric dispersion models, COST Action 710, CEC Publication EUR 18195, pp. 145–265, 1998.

Stull, R.B., 1991: Static Stability - An Update. Bull. Amer. Meteorol. Soc. 72, 1521-1529.

Extra slides

Doppler spectral width

Profiler reflectivity and spectral width patterns for a “typical” day

Methods to Determine the Mixed-Layer Depth from Soundings?

There are several methods to determine the height of the stable boundary layer.

from Seibert et al. (1998)

Classic – how does a profiler detect the

ABL? Reflectivity is roughly the

product of humidity gradient and turbulence intensity

Deep layer• Note deep entrainment

signatures

Residual layer• Can fool simple

automated algorithms

Low humidity• Weakens signal

Weak inversion, cloud• Broad or weak inversion• “Deep” but non-

precipitating cloud• Ceilometer aids greatly

in interpretation

Multiple layers• Note correlation of layers

to soundings

Coastal BL with sea breeze

• Pease day 215 2002

Marine BL• Appledore day 181 2002